Calvin’s Big Mistake

The argument has stretched for weeks over on KQED, and I believe Calvin has finally revealed enough about his model for me to find a fatal flaw.

As previously reported, Calvin argues that the net ground reaction force acting on a bike as it leans must remain aligned with the midplane of the bike. This then means that the ground reaction force cannot create a moment about the steering axis through trail. With gyroscopic effect already minimized, and trail now neutralized, Calvin’s tire theory can come to the rescue.

The problem, however, is that the net ground reaction force does not remain aligned with the midplane of the bike unless the bike is modeled as a point mass on a massless rod. As soon as a finite mass distribution is considered, Calvin’s fundamental premise falls apart.

In an effort to induce Calvin to concede this flaw, I have derived expressions for the ground reaction force orientation for two different mass distributions: a point mass and a uniform rod, and asked Calvin to point out any flaws in my derivation.

So far, he has not managed to find any, and has simply reiterated his reasoning instead. Therefore, I have done my best to follow his reasoning and find where it goes awry. It turns out that Calvin appears to have made a common undergraduate mistake by forgetting to use the Parallel Axis Theorem when he inserts the mass moment of inertia into his derivation.

The details are in the images below. The outdented text is Calvin’s original explanation, and the indented text and equations are my detailed reply:

There we have it. Time will tell if it has any impact on Calvin’s thinking.